Permutation Bo

Problem Description
There are two sequences h1∼hn and c1∼cn. h1∼hn is a permutation of 1∼n. particularly, h0=hn+1=0.

We define the expression [condition] is 1 when condition is True,is 0 when condition is False.

Define the function f(h)=∑ni=1ci[hi>hi−1 and hi>hi+1]

Bo have gotten the value of c1∼cn, and he wants to know the expected value of f(h).

Input
This problem has multi test cases(no more than 12).

For each test case, the first line contains a non-negative integer n(1≤n≤1000), second line contains n non-negative integer ci(0≤ci≤1000).

Output
For each test cases print a decimal - the expectation of f(h).

If the absolute error between your answer and the standard answer is no more than 10−4, your solution will be accepted.

Sample Input
4
3 2 4 5
5
3 5 99 32 12

Sample Output
6.000000
52.833333

2个回答

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